Academic age

author_w_year <- author_paper_affiliations %>%
  left_join(author_metadata) %>%
  select(paperid, authorid, authorsequencenumber, year_first_paper)

## Joining, by = "authorid"

papers_w_age <- papers %>%
  # only take papers with OA status for now
  filter(!is.na(is_oa)) %>%
  left_join(author_w_year) %>%
  mutate(current_age = year - year_first_paper)

## Joining, by = "paperid"

age_dist <- papers_w_age %>%
  filter(year == 2018) %>%
  distinct(authorid, current_age) %>%
  count(current_age) %>%
  collect()

age_dist %>%
  ggplot(aes(current_age, n)) +
  geom_col() +
  scale_y_continuous(labels = function(x) format(x,
                                                 big.mark = ".",
                                                 decimal.mark = ",")) +
  labs(y = "Number of researchers", title = "Current age of researchers in 2018",
       caption = "Only taking authors on papers that have an OA status into account")

age_trunc <- papers_w_age %>%
  filter(current_age <= 50 | current_age > 0) %>%
  distinct(year, paperid, is_oa, oa_status, current_age, authorsequencenumber)

# make age groups
age_oa <- age_trunc %>%
  mutate(age_group = case_when(
    current_age > 0 & current_age < 10 ~ "1-9 years",
    current_age >= 10 & current_age < 20 ~ "10-19 years",
    current_age >= 20 & current_age < 30 ~ "20-39 years",
    current_age >= 30 & current_age < 40 ~ "30-39 years",
    current_age >= 40 & current_age < 50 ~ "40-49 years",
    current_age >= 50 & current_age < 60 ~ "50-59 years",
    TRUE ~ "60+ years"
  )) %>%
  group_by(year, age_group) %>%
  summarise(oa_share = mean(as.numeric(is_oa))) %>%
  collect()

age_oa %>%
  ggplot(aes(as_year(year), oa_share, colour = age_group, group = age_group)) +
  geom_point() +
  geom_line() +
  scale_y_continuous(labels = function(x) scales::percent(x, accuracy = 1)) +
  theme_bw() +
  labs(x = NULL, y = "OA share", title = "OA share over time", colour = NULL)

Group into first, last, and middle author

age_base <- papers %>% 
  select(paperid, SDG_label, year, is_oa) %>% 
  left_join(author_paper_affiliations_w_groups) %>% 
  left_join(author_metadata) %>% 
  select(paperid, SDG_label, year, author_position, authorid, 
         year_first_paper, is_oa, paper_author_cat)

## Joining, by = "paperid"

## Joining, by = "authorid"

age_cohorts <- age_base %>% 
  group_by(year, authorid) %>% 
  mutate(current_age = year - year_first_paper) %>% 
  filter(current_age > 0) %>% 
  mutate(age_cohort = case_when(
    year_first_paper < 1960 ~ NA_character_,
    year_first_paper < 1970 ~ "1960-1969",
    year_first_paper < 1980 ~ "1970-1979",
    year_first_paper < 1990 ~ "1980-1989",
    year_first_paper < 2000 ~ "1990-1999",
    year_first_paper < 2010 ~ "2000-2009",
    TRUE ~ "2010-2017"
  )) %>% 
  ungroup()

age_oa_cohort <- age_cohorts %>% 
  group_by(year, age_cohort, SDG_label) %>%
  summarise(oa_share = mean(as.numeric(is_oa))) %>%
  collect()

age_oa_cohort %>%
  filter(age_cohort != "NA") %>% 
  ggplot(aes(as_year(year), oa_share, colour = SDG_label)) +
  geom_point() +
  geom_line() +
  facet_wrap(vars(age_cohort)) +
  scale_y_continuous(labels = function(x) scales::percent(x, accuracy = 1)) +
  theme_bw() +
  labs(x = NULL, y = "OA share", title = "OA share by year of first paper",
       colour = NULL)

age_oa_cohort %>%
  filter(age_cohort != "NA") %>% 
  ggplot(aes(as_year(year), oa_share, colour = age_cohort)) +
  geom_point() +
  geom_line() +
  facet_wrap(vars(SDG_label), nrow = 2) +
  scale_y_continuous(labels = function(x) scales::percent(x, accuracy = 1)) +
  theme_bw() +
  theme(legend.position = c(.8, .2)) +
  labs(x = NULL, y = "OA share", title = "OA share over time", colour = NULL)

By author position

age_oa_positions <- age_cohorts %>% 
  # only consider multi author papers
  filter(paper_author_cat == "multi", age_cohort != "1960-1969") %>% 
  group_by(year, age_cohort, SDG_label, author_position) %>%
  summarise(oa_share = mean(as.numeric(is_oa)),
            n = n()) %>%
  collect()

age_oa_positions %>%
  filter(age_cohort != "NA", year < 2020) %>% 
  ggplot(aes(as_year(year), oa_share, colour = age_cohort)) +
  geom_point() +
  geom_line() +
  facet_grid(rows = vars(fix_sdg(SDG_label)), cols = vars(author_position)) +
  scale_y_continuous(labels = function(x) scales::percent(x, accuracy = 1)) +
  theme_bw() +
  theme(legend.position = c(.9385, .083)) +
  labs(x = NULL, y = "OA share", title = "OA share over time", colour = NULL,
       caption = "Only considering multi author papers. Dropping 2020 because of low cell counts")

Findings:

MEdicine for first authors: very narrow bandwith, compared to last and middle authors - age is not very relevant there.
medicine last authors: younger researchers (from 2000) initially considerably lower OA rate, more or less caught up with the rest
Overall: OA share is lower for younger authors

Individual prestige

Issue: the current perspective is agnostic to the timeline: citations are aggregated towards each author. To make a claim about whether being prestigious makes you publish OA we would need to know the citations prior to publication. but this data is not available in MAG. It could be generated from the raw graph: counting the links to each paper per year. But probably out of scope for now.

# get the ratio of OA publications by author
author_oa <- author_paper_affiliations %>% 
  left_join(papers) %>%
  # restrict to unpaywall set
  filter(!is.na(is_oa)) %>% 
  group_by(authorid) %>% 
  summarise(oa_pubs = sum(as.numeric(is_oa))) %>% 
  left_join(author_metadata, .)

## Joining, by = "paperid"

## Joining, by = "authorid"

author_oa <- author_oa %>% 
  select(authorid, papercount, year_first_paper, n_citations_norm, 
         n_unique_co_authors, mean_co_authors, oa_pubs) %>% 
  mutate(oa_share = oa_pubs / papercount)

author_oa %>% 
  filter(papercount >= 5) %>% 
  summarise(oa_cit = cor(oa_share, n_citations_norm),
            oa_n_pap = cor(oa_share, papercount),
            oa_u_co_auth = cor(oa_share, n_unique_co_authors),
            oa_m_co_autho = cor(oa_share, mean_co_authors),
            oa_age = cor(oa_share, year_first_paper)) %>% 
  collect() %>% 
  knitr::kable()

oa_cit	oa_n_pap	oa_u_co_auth	oa_m_co_autho	oa_age
-0.0491943	-0.1140835	-0.0125805	0.0135733	0.2664612

Two smallish effects:

more overall publications are associated with a lower share of OA publications
older academics have a higher OA share (in line with above)

Citations and co-authors have no effect on this global level.

This should be further broken down into disciplines, and if somehow possible across time.

Important note: the analysis of OA on the individual level will likely come from the paper perspective: factors influencing whether a given paper is OA. So different than the QSS paper, which looks at which author characteristics are associated with more OA publications.

Difficulty: time perspective. All variables would need to have a time-wise aspect, i.e. should relate to before the paper was published.

Institutional prestige

leiden_small_local <- leiden %>%
  filter(Field == "All sciences", Frac_counting == 1) %>%
  select(University, Country, Period, P_top10, PP_top10, impact_P, P_OA,
         PP_OA) %>% 
  collect() %>% 
  mutate(across(c(P_top10, PP_top10, impact_P, P_OA, PP_OA), as.numeric),
         last_year_of_period = str_extract(Period, "\\d{4}$"))

affil_leiden_key <- read_csv2(
  here::here("data/leiden matching/matching_leiden.csv")
)

## ℹ Using "','" as decimal and "'.'" as grouping mark. Use `read_delim()` for more control.

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   affiliationid = col_double(),
##   normalizedname = col_character(),
##   displayname = col_character(),
##   university_normalized = col_character(),
##   University = col_character(),
##   Country = col_character(),
##   university_normalized_leiden = col_character()
## )

What is the question here? could simply take leiden ranking to investigate connex between prestige and oa publication. Interesting could be cross level effects: are effects of age and gender (if they exist) different for more prestiguous institutions?

maybe do this connex between prestige and OA first, then dig into further stuff BUT: special question here is the contribution towards the SDG stuff, and maybe within that the OA share.

maybe also more interesting to look into the type of OA publication, not simply oa yes or no.

papers_per_affiliation_per_sdg <- papers %>% 
  left_join(author_paper_affiliations) %>% 
  left_join(affils) %>% 
  group_by(authorid, paperid) %>% 
  mutate(frac_value = 1/n()) %>% 
  group_by(affiliationid, year, SDG_label) %>% 
  summarise(n_frac_papers = sum(frac_value, na.rm = TRUE),
            n_frac_oa_papers = sum(frac_value * as.numeric(is_oa), na.rm = TRUE),
            n_frac_citations = sum(frac_value * citations_norm, na.rm = TRUE)) %>% 
  collect()

## Joining, by = "paperid"

## Joining, by = c("citationcount", "affiliationid")

papers_per_affiliation_per_w_leiden <- papers_per_affiliation_per_sdg %>%
  mutate(affiliationid = as.numeric(affiliationid)) %>% # needed for merging
  left_join(affil_leiden_key) %>%
  left_join(leiden_small_local)

## Joining, by = "affiliationid"

## Joining, by = c("University", "Country")

affil_oa <- papers_per_affiliation_per_w_leiden %>% 
  mutate(match_period = year == last_year_of_period) %>% 
  filter(match_period) %>% 
  mutate(oa_share = n_frac_oa_papers / n_frac_papers)

affil_oa %>% 
  group_by(year) %>% 
  filter(n_frac_papers > 50) %>% 
  summarise(cor = cor(oa_share, PP_OA, use = "pairwise.complete.obs")) %>% 
  knitr::kable()

year	cor
2009	0.6684618
2010	0.6678632
2011	0.6931630
2012	0.6374927
2013	0.7103419
2014	0.6956760
2015	0.7043756
2016	0.7502294
2017	0.7753870
2018	0.7962919

This gives the overall picture.

affil_oa %>% 
  filter(year == 2018, n_frac_papers > 50) %>% 
  ggplot(aes(PP_OA, oa_share)) +
  geom_point() +
  labs(x = "OA share (leiden)", y = "OA share SDG", caption = "Data for 2018")

Now by SDG

affil_oa %>% 
  group_by(year, SDG_label) %>% 
  filter(n_frac_papers > 50) %>% 
  summarise(cor = cor(oa_share, PP_OA, use = "pairwise.complete.obs")) %>% 
  ggplot(aes(year, cor, colour = SDG_label)) +
  geom_line() +
  geom_point() +
  labs(y = "Correlation between OA shares in SDG & Leiden", x = NULL, 
       colour = NULL)

## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

The association between overall OA level publications and SDG OA level is rising, in particular for SDG 13.

Now correlate with prestige

affil_oa %>% 
  group_by(year, SDG_label) %>% 
  filter(n_frac_papers > 50) %>% 
  summarise(cor = cor(oa_share, P_top10, use = "pairwise.complete.obs")) %>% 
  ggplot(aes(year, cor, colour = SDG_label)) +
  geom_line() +
  geom_point() +
  scale_y_continuous(limits = c(0, .6)) +
  labs(y = "Correlation between OA shares in SDG & P_top10", x = NULL, 
       colour = NULL)

## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

affil_oa %>% 
  group_by(year, SDG_label) %>% 
  filter(n_frac_papers > 50) %>% 
  summarise(cor = cor(oa_share, PP_top10, use = "pairwise.complete.obs")) %>% 
  ggplot(aes(year, cor, colour = SDG_label)) +
  geom_line() +
  geom_point() +
  scale_y_continuous(limits = c(0, .6)) +
  labs(y = "Correlation between OA shares in SDG & PP_top10", x = NULL, 
       colour = NULL)

## `summarise()` has grouped output by 'year'. You can override using the `.groups` argument.

Very interesting: while in 2008, the prestige of a university (measured both in absolute (P_top10) and relative (PP_top10) terms was associated with the share of OA publications within SDG, this association has been declining. Points to a proliferation of OA? This might be in opposition to our expectations, i.e. when we expected that OA is only feasible for well-resourced actors?

Look at this in terms of types of OA, and with percentiles of the leiden ranks.

Percentile ranks

pdata <- affil_oa %>% 
  filter(!is.na(P_top10), n_frac_papers > 50) %>% 
  group_by(Period) %>% 
  mutate(across(c(P_top10, PP_top10, P_OA, PP_OA, impact_P), cut_quartiles))

plot_over_time <- function(df, indicator, y_var) {
  df %>% 
    group_by(SDG_label, year, {{indicator}}) %>% 
    mutate(y_median = median({{y_var}}, na.rm = TRUE)) %>% 
    ggplot(aes(as_year(year), y_median, colour = {{indicator}})) +
    geom_line() +
    facet_wrap(vars(SDG_label)) +
    scale_y_continuous(labels = scales::percent) +
    guides(colour = guide_legend(reverse = TRUE)) +
    labs(x = NULL)
}

pdata %>%
  plot_over_time(indicator = P_top10, oa_share) +
  labs(y = "Share of SDG papers which are OA")

pdata %>%
  plot_over_time(indicator = PP_top10, oa_share) +
  labs(y = "Share of SDG papers which are OA")

pdata %>%
  plot_over_time(indicator = impact_P, oa_share) +
  labs(y = "Share of SDG papers which are OA",
       title = "# of publications per university vs SDG OA")

Types of OA

step1 <- papers %>% 
  left_join(author_paper_affiliations) %>% 
  left_join(affils) %>% 
  group_by(authorid, paperid) %>% 
  mutate(frac_value = 1/n())

## Joining, by = "paperid"

## Joining, by = c("citationcount", "affiliationid")

oa_type_per_affiliation_per_sdg <- step1 %>% 
  group_by(affiliationid, year, SDG_label) %>% 
  count(provider_cat, wt = frac_value)

totals <- step1 %>% 
  group_by(affiliationid, year, SDG_label) %>% 
  summarise(n_frac_papers = sum(frac_value, na.rm = TRUE))

oa_type_per_affiliation_per_sdg <- oa_type_per_affiliation_per_sdg %>% 
  left_join(totals)

## Joining, by = c("affiliationid", "year", "SDG_label")

oa_type_per_affiliation_per_sdg_local <- oa_type_per_affiliation_per_sdg %>% 
  filter(n_frac_papers > 50, !is.na(provider_cat)) %>% 
  collect()

oa_type_affiliation_leiden <- oa_type_per_affiliation_per_sdg_local %>%
  mutate(affiliationid = as.numeric(affiliationid)) %>% # needed for merging
  left_join(affil_leiden_key) %>%
  left_join(leiden_small_local) %>% 
  # remove those institutions that are not in leiden ranking
  filter(!is.na(University), year == as.numeric(last_year_of_period))

## Joining, by = "affiliationid"

## Joining, by = c("University", "Country")

oa_type_affiliation_leiden %>% 
  filter(provider_cat != "Not OA") %>% 
  mutate(oa_share = n/n_frac_papers) %>% 
  group_by(year, SDG_label, provider_cat) %>% 
  summarise(cor = cor(oa_share, P_top10, use = "pairwise.complete.obs")) %>% 
  ggplot(aes(year, cor, colour = provider_cat)) +
  geom_line() +
  geom_point() +
  facet_wrap(vars(SDG_label)) +
  theme(legend.position = "top") +
  labs(title = "Correlation between share of papers in category & P_top10",
       colour = NULL)

## `summarise()` has grouped output by 'year', 'SDG_label'. You can override using the `.groups` argument.

What does this mean, especially the green negative correlation?

oa_type_affiliation_leiden %>% 
  filter(provider_cat != "Not OA") %>% 
  mutate(oa_share = n/n_frac_papers) %>% 
  group_by(year, SDG_label, provider_cat) %>% 
  summarise(cor = cor(oa_share, PP_top10, use = "pairwise.complete.obs")) %>% 
  ggplot(aes(year, cor, colour = provider_cat)) +
  geom_line() +
  geom_point() +
  facet_wrap(vars(SDG_label)) +
  theme(legend.position = "top") +
  labs(title = "Correlation between share of papers in category & PP_top10",
       colour = NULL)

## `summarise()` has grouped output by 'year', 'SDG_label'. You can override using the `.groups` argument.

p <- oa_type_affiliation_leiden %>% 
  filter(provider_cat != "Not OA", year == 2018) %>% 
  group_by(year, SDG_label, affiliationid) %>% 
  mutate(oa_share = n/sum(n)) %>% 
  ggplot(aes(P_top10, oa_share, colour = provider_cat)) +
  geom_point(size = .7, alpha = .4) +
  scale_x_log10() +
  geom_smooth() +
  facet_wrap(vars(SDG_label)) +
  scale_y_continuous(labels = scales::percent) +
  theme(legend.position = "top") +
  labs(y = "Share of papers in category", colour = NULL,
       title = "Association between type of OA and institutional prestige (2018)")
p

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Share of papers which are journal and repository hosted is similar across institutions and SDGs
Lower ranked universities have a low fraction of repository only, but a higher fraction of journal only OA publications.
High ranked institutions do not have a high share of journal only publications

Further investigating the split between low prestige universities in SDG 3:

p <- oa_type_affiliation_leiden %>% 
  filter(provider_cat != "Not OA", year == 2018, SDG_label == "SDG_3") %>% 
  group_by(year, affiliationid) %>% 
  mutate(oa_share = n/sum(n)) %>% 
  ggplot(aes(P_top10, oa_share, colour = provider_cat, size = n_frac_papers)) +
  geom_point(alpha = .4) +
  scale_x_log10()

p <- p + aes(label = Country, text = University)
plotly::ggplotly(p)

Unclear where this split comes from. It is not related to size (in terms of number of publications), and seems also unrelated to country/continent.

Further things to look at:

does this translate to certain types of journals, i.e. according to APC or IF?
how is this over time?

Gender analysis

gender_base <- papers %>% 
  select(paperid, SDG_label, year, is_oa) %>% 
  left_join(author_paper_affiliations_w_groups) %>% 
  left_join(author_metadata) %>% 
  select(paperid, SDG_label, year, author_position, authorid, 
         is_oa, paper_author_cat, gender) %>% 
  filter(!is.na(is_oa)) # restrict to unpaywall set only

## Joining, by = "paperid"

## Joining, by = "authorid"

gender_rate <- gender_base %>% 
  group_by(SDG_label, year, gender) %>% 
  count(is_oa) %>% 
  mutate(prop = n/sum(n)) %>% 
  collect()

Visalise oa rate per gender over time

gender_rate %>% 
  filter(is_oa, gender != "unknown", year < 2019) %>% 
  ggplot(aes(as_year(year), prop, colour = gender)) +
  geom_line() +
  geom_point() +
  facet_wrap(vars(SDG_label))

This does not show big differences. At least in health, papers by women tend to have slightly higher OA rates.

But: what are we showing here? What is the y axis exactly? Should we maybe show how the number of female authors, or how the gender split in the authors of a given paper is related to OA? would make more sense than overall. Do this only for a specific year.

It will also be more productive to visualise this for first and last authors only.

Split for author positions

gender_rate_p_position <- gender_base %>% 
  filter(!is.na(is_oa), gender != "unknown") %>% # restrict to unpaywall set only
  group_by(SDG_label, year, gender, author_position) %>% 
  count(is_oa) %>% 
  mutate(prop = n/sum(n)) %>% 
  collect()

gender_rate_p_position %>% 
  filter(is_oa, year < 2019) %>% 
  ggplot(aes(as_year(year), prop, colour = gender)) +
  geom_line() +
  geom_point() +
  facet_grid(rows = vars(SDG_label),
             cols = vars(author_position))

Also here there is no difference. What does this show? The proportion of papers which are OA per gender, SDG, author position and year.

Then, lets look at this in terms of papers

# only do this for papers where we have gender for all authors
gender_ratio_p_paper <- gender_base %>% 
  select(paperid, gender) %>% 
  group_by(paperid) %>% 
  mutate(all_genderized = sum(as.numeric(gender == "unknown")) == 0) %>% 
  filter(all_genderized) %>% 
  count(gender) %>% 
  mutate(prop = n/sum(n)) %>% 
  ungroup() %>% 
  filter(gender == "female") %>% 
  rename(prop_female = prop)


gender_oa_papers <- gender_ratio_p_paper %>% 
  left_join(papers) %>% 
  # it could be interesting though to look at this via regression -> then keep
  # more variables
  select(paperid, prop_female, year, is_oa, SDG_label) %>% 
  filter(!is.na(is_oa))

## Joining, by = "paperid"

gender_by_sdg <- gender_oa_papers %>% 
  group_by(year, is_oa, SDG_label) %>% 
  summarise(mean_prop_female = mean(prop_female)) %>% 
  collect()

gender_by_sdg %>% 
  ggplot(aes(as_year(year), mean_prop_female, colour = is_oa)) +
  geom_line() +
  geom_point() +
  facet_wrap(vars(fix_sdg(SDG_label)), nrow = 2) +
  scale_y_continuous(labels = function(x) scales::percent(x, 1),
                     limits = c(.45, .60)) +
  labs(x = NULL, y = "Mean share of female authors on publications",
       caption = "Including publications with at least two authors") +
  theme_bw() +
  theme(legend.position = c(.8, .2))

Very interesting: OA papers generally have a lower share of female authors. The reasons for this are probably related with general factors of OA publishing, in complex patterns (institutional prestige, funding, academic age, country differences, etc.). This is why it would be good to do a full model.

What to look at now: author position, i.e. whether authors with female first authors have more OA, or with male last authors, etc.

gender_oa_position <- gender_base %>% 
  filter(paper_author_cat != "single", author_position != "middle_author",
         gender != "unknown") %>% 
  select(paperid, SDG_label, year, author_position, is_oa, gender) %>% 
  group_by(year, SDG_label, author_position, gender) %>% 
  count(is_oa) %>% 
  mutate(prop = n/sum(n)) %>% 
  filter(is_oa) %>% 
  rename(prop_oa = prop) %>% 
  collect()

pdata <- gender_oa_position %>% 
  select(-n) %>% 
  pivot_wider(names_from = gender, values_from = prop_oa) %>% 
  mutate(diff_from_male = female - male)

pdata %>% 
  filter(year < 2020) %>% 
  # filter(author_position == "first_author") %>% 
  ggplot(aes(as_year(year), diff_from_male, colour = fix_sdg(SDG_label))) +
  geom_line() +
  geom_point() + 
  facet_wrap(vars(author_position)) +
  scale_y_continuous(labels = scales::percent) +
  theme_bw() +
  theme(legend.position = "top") +
  labs(title = "Difference in OA publishing between genders",
       x = NULL, y = "Difference from males", colour = NULL)

A value of x% means that in that year, the share of papers with women as first/last authors which were published OA is X percentage points higher, e.g. male first authors published 50% of their papers OA, females 52% for X = 2.

Why is the difference to the above plot so big? Differences in single authors? This view here only includes papers with at least two authors, the above includes all.

To do: the above (first one) but only with papers which are not single author papers

# only do this for papers where we have gender for all authors
gender_ratio_p_paper_no_single <- gender_base %>% 
  filter(paper_author_cat != "single") %>% 
  select(paperid, gender) %>% 
  group_by(paperid) %>% 
  mutate(all_genderized = sum(as.numeric(gender == "unknown")) == 0) %>% 
  filter(all_genderized) %>% 
  count(gender) %>% 
  mutate(prop = n/sum(n)) %>% 
  ungroup() %>% 
  filter(gender == "female") %>% 
  rename(prop_female = prop)


gender_oa_papers_no_single <- gender_ratio_p_paper_no_single %>% 
  left_join(papers) %>% 
  # it could be interesting though to look at this via regression -> then keep
  # more variables
  select(paperid, prop_female, year, is_oa, SDG_label) %>% 
  filter(!is.na(is_oa))

## Joining, by = "paperid"

gender_by_sdg_no_single <- gender_oa_papers_no_single %>% 
  group_by(year, is_oa, SDG_label) %>% 
  summarise(mean_prop_female = mean(prop_female)) %>% 
  collect()

gender_by_sdg_no_single %>% 
  ggplot(aes(as_year(year), mean_prop_female, colour = is_oa)) +
  geom_line() +
  geom_point() +
  facet_wrap(vars(fix_sdg(SDG_label)), nrow = 2) +
  scale_y_continuous(labels = function(x) scales::percent(x, 1)) +
  labs(x = NULL, y = "Mean share of female authors on publications",
       caption = "Including publications with at least two authors") +
  theme_bw() +
  theme(legend.position = c(.8, .2))

The effect is already smaller than above, but still there. So single author papers are not the only source of confounding here.

I also checked the above approach (with small differences) for middle authors, but there was not difference there. So where does this gap come from? Why do OA papers have lower rates of females as authors, although rates of females for first and last positions have little effect?

For the gender rate per paper, we only include papers for which we have gender for all authors. Maybe this distorts, i.e. reduces the set considerably?

Share of female authorships by OA vs non-OA

gender_rate_2 <- gender_base %>% 
  group_by(SDG_label, year, is_oa) %>% 
  count(gender) %>% 
  filter(gender != "unknown", year < 2019) %>% 
  mutate(prop = n/sum(n)) %>% 
  collect()